Characterizations of the commutators involving idempotents in certain subrings of $M_{2}(\mathbb{Z})$

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Date

2023

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Tubitak Scientific & Technological Research Council Turkey

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Department of Social Sciences for University wide Courses
Our department offers compulsory courses “Turkish Language” and “Principles of Atatürk and History of Turkish Revolution” as envisaged by the Council of Higher Education as well as History of Civilization course to all the students at our university. Along with these compulsory courses, the department offers general elective courses comprising subjects such as social responsibility tasks, Women studies, culture and history. The purpose of compulsory Principles of Ataturk and History of Turkish Revolution course is to introduce and convey the foundation and fundamental values of the Republic of Turkey to the new generations and the objective of Turkish Language course is to study on our language with modern methods within the scope of the subjects such as language, literature, culture etc.

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Abstract

In this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator [E1, E2] = E1E2 - E2E1 involving idempotents E1, E2 in certain subrings of M2(Z).

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OZDIN, Tufan/0000-0001-8081-1871

Keywords

Clean (Nil-clean) element, commutator, idempotent, unit element, Nilpotent, unit-regular element

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0

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Q2

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Q2

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Volume

47

Issue

5

Start Page

1498

End Page

1507

URI

https://doi.org/10.55730/1300-0098.3443
 https://hdl.handle.net/20.500.14411/2551

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